Question

How much energy is released if two kilograms of mass are converted to its equivalent amount of
energy? (use c = 3 x 10^8 m / s)
Answers below:
6 × 10^8 J

2 × 10^17 J

4 × 10^4 J

2 x 10^14 J

Answer 1

To calculate the energy released when mass is converted to energy, you can use Einstein's equation:

\[ E = mc^2 \]

where:
- \( E \) is the energy (in joules),
- \( m \) is the mass (in kilograms),
- \( c \) is the speed of light (approximately \( 3 \times 10^8 \) m/s).

Given:
- \( m = 2 \) kg,
- \( c = 3 \times 10^8 \) m/s.

Now plug in the values:

\[
E = (2 \, \text{kg}) \times (3 \times 10^8 \, \text{m/s})^2
\]

Calculating \( c^2 \):

\[
(3 \times 10^8 \, \text{m/s})^2 = 9 \times 10^{16} \, \text{m}^2/\text{s}^2
\]

Now calculate \( E \):

\[
E = 2 \times 9 \times 10^{16} = 18 \times 10^{16} \, \text{J} = 1.8 \times 10^{17} \, \text{J}
\]

Therefore, rounding to two significant figures, the energy released is approximately:

\[
2 \times 10^{17} \, \text{J}
\]

So the correct answer is:

**2 × 10^17 J**.